Gaps left by simple closed geodesics on surfaces

This talk concerns joint work with Hugo Parlier. For a Riemann surface endowed with a hyperbolic metric, J. Birman and C. Series have shown that the set of all points lying on any simple closed geodesic is nowhere dense on the surface. (This set is sometimes referred to as the Birman-Series set).

The talk will discuss the existence of positive constants $C_g$, such that for any surface of genus $g$, the complementary region to the Birman-Series set allows an isometrically embedded disk with radius $C_g$. The behavior of $C_g$ as function of $g$, as well as some bounds will be discussed.

The talk will also discuss a new algorithm for the enumeration of the simple closed goedesics.